Geodesic
An algorithm for approximating a discrete signal with a small number of harmonics with decreasing amplitudes
Numerical methods and programming, Tome 25 (2024) no. 3, pp. 274-291

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An algorithm for approximating an arbitrary discrete signal by a trigonometric polynomial with decreasing harmonics in amplitude is proposed. It has an algorithmic complexity of O(NR(L + log2 N)), where L is the length of the polynomial, N is the length of the set of samples of the original signal, and NR is the length of the frequency basis of the fast Fourier transform (FFT) algorithm. The flowcharts of the developed algorithms, the source texts of Python programs, and the results of numerical experiments are presented. The developed algorithms can be applied to improve domestic technologies in the field of electronics and software, as well as included in the curricula of engineering specialties.
Keywords: trigonometric polynomial, sequential harmonic subtraction method, high resolution, trigonometric approximation, least squares method, digital signal processing (DSP), the amplitude spectrum of the signal, data analysis, spectrum spreading.
Mots-clés : fast Fourier transform (FFT) 
@article{VMP_2024_25_3_a2,
     author = {O. V. Osipov},
     title = {An algorithm for approximating a discrete signal with a small number of harmonics with decreasing amplitudes},
     journal = {Numerical methods and programming},
     pages = {274--291},
     publisher = {mathdoc},
     volume = {25},
     number = {3},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2024_25_3_a2/}
}
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O. V. Osipov. An algorithm for approximating a discrete signal with a small number of harmonics with decreasing amplitudes. Numerical methods and programming, Tome 25 (2024) no. 3, pp. 274-291. http://geodesic.mathdoc.fr/item/VMP_2024_25_3_a2/